Singular valuations and the Hadwiger theorem on convex functions
Metric Geometry
2024-10-16 v4
Abstract
We give a characterization of smooth, rotation and dually epi-translation invariant valuations and use this result to obtain a new proof of the Hadwiger theorem on convex functions. We also give a description of the construction of the functional intrinsic volumes using integration over the differential cycle and provide a new representation of these functionals as principal value integrals with respect to the Hessian measures.
Cite
@article{arxiv.2209.05158,
title = {Singular valuations and the Hadwiger theorem on convex functions},
author = {Jonas Knoerr},
journal= {arXiv preprint arXiv:2209.05158},
year = {2024}
}
Comments
40 pages, slight change of notation, includes a discussion under which conditions a given valuation admits a proper integral representation